Question

If \([A]_{3 \times 2} [B]_{x \times y} = [C]_{3 \times 1}\), then \( x \) and \( y \) are:

• A. $x = 1, y = 3$
• B. $x = 2, y = 1$
• C. $x = 3, y = 3$
• D. $x = 3, y = 1$

Answer 1

The Correct Option is B

Given the matrices:

\[ [A]_{3 \times 2}, \quad [B]_{x \times y}, \quad [C]_{3 \times 1}. \]

For matrix multiplication \([A][B]\) to be defined, the number of columns of \(A\) must equal the number of rows of \(B\), so:

\[ x = 2. \]

The resulting product \([A][B]\) will have dimensions \(3 \times y\), which must match \([C]_{3 \times 1}\), so:

\[ y = 1. \]

Thus:

\[ x = 2, \quad y = 1. \]

The correct option is:

\[ x = 2, \, y = 1. \]